Empirical observations of dynamic dilemma zones at signalized intersections

Transcription

1 Liu, Chang, Tao, Hicks, and Tabacek Empirical observations of dynamic dilemma zones at signalized intersections Yue Liu, Gang-Len Chang, Ph.D., Professor, Department of Civil Engineering The University of Maryland, College Park, MD 074 Tel: (301) Ruihua Tao, Ph.D., Thomas Hicks, P.E., Director, Eric Tabacek, Division Chief, Maryland State Highway Administration Office of Traffic and Safety 7491 Connelley Drive, Hanover, MD 1076 Word Count: 3, tables + 8 figures Submitted to the 86 th meeting of the Transportation Research Board for presentation and publication July 006

2 Liu, Chang, Tao, Hicks, and Tabacek ABSTRACT In this paper the author presents the results of our empirical study on the distribution of dilemma zones for different groups of drivers at signalized intersections. Using a specially designed video-based system, this study has conducted extensive field observations of 113 drivers responses to a yellow phase at six intersections of high accident frequency, including all critical data such as the speed evolution during the yellow phase, the acceleration/deceleration rates, and the approximate reaction time to an encountered yellow phase. Our empirical results have revealed that the dilemma zone is dynamic in nature with its location varying with the driving populations, and the commonly used practice of extending the yellow phase duration recommended may not eliminate all the dilemma zones. Two types of strategies which can effectively eliminate the dynamic dilemma zones are also designed to improve intersection safety. Key words: yellow phase, dilemma zone, driver grouping

3 Liu, Chang, Tao, Hicks, and Tabacek 3 1. INTRODUCTION Over the past several decades, traffic signal-related crashes constituted about 30 percent of the total accidents on Maryland state routes (e.g., 33% in 00 and 34% in 003). Among those, about 0 percent involved red-light-runnings, which caused either fatal rear-end or side-crash collisions (1). Despite the significant progress of safety improvement programs implemented by responsible agencies over the recent years, traffic signal related crashes have not been significantly reduced. In Maryland and many other states, one of the main contributors to signal-related accidents is the existence of a dilemma zone at signalized intersections. Thus, understanding the dynamic nature of intersection dilemma zones so as to design counter measures has emerged as one of the imperative research issues in the traffic safety community (). As defined in the ITE handbook (3), a dilemma zone is a range, in which a vehicle approaching the intersection during the yellow phase can neither safely clear the intersection, nor stop comfortably at the stop-line (see Figure 1). The existing practice (3) for computing the dilemma zone is based on the following kinematics equation: Cannot stop x c x 0 Cannot pass Dilemma Zone x dz = x c x 0 FIGURE 1 A graphical illustration of the dilemma zone at signalized intersections x dz v 1 = x x a c 0 * 0 = v0 + v * 0 + ( w + L) 1 ( 1) a where: x c = the critical distance for a smooth stop under the maximum deceleration rate; x 0 = the critical distance for pass under the maximum acceleration rate; = duration of the yellow phase (sec); 1 = reaction time-lag of the driver-vehicle complex (sec); = decision-making time of a driver (sec); v 0 = approaching speed of vehicles (ft/sec); a 1 = average vehicle acceleration rate ( ft / s ); * a 1 = maximum acceleration rate of the approaching vehicles ( ft / s ); a = average vehicle deceleration rate ( ft / s ); (1)

4 Liu, Chang, Tao, Hicks, and Tabacek 4 * a = maximum deceleration rate of the approaching vehicles ( ft / s ); w = intersection width (ft); and L = average vehicle length (ft). Note that both the length and the location of a dilemma zone may vary with the speed of the approaching vehicles, driver reaction times, and vehicle acceleration/deceleration rates. Under the same condition, one can use a longer yellow phase to eliminate the dilemma zone if both the reaction time and vehicle acceleration/deceleration rates are identical among the driving populations. However, in reality the parameters, 1 and, which represent the perception and reaction times may vary significantly among driving populations. The * * maximum acceleration/deceleration rates (denoted as a 1 and a ), and the approaching speed ( v 0 ) may also be distributed in a wide range among different driver and vehicle groups. For example, young and aggressive drivers tend to exercise a higher speed and have a shorter perception-reaction time than older and/or conservative drivers when approaching the intersection. The acceleration/deceleration rates of sport cars are certainly different from those of family sedans (4). Hence, the actual dilemma zone at an intersection is more likely to be a distribution rather than a constant as computed in existing practices. Thus, an increase in the yellow duration alone may not be sufficient for eliminating all such dilemma zones for different driving populations. In review of the literature, it is evident that the first intersection dilemma zone model, also termed as Type-I Dilemma was developed by Gazis, Herman, and Maraduin (5) in their land-marking paper, called The GHM Model. They also indicated that incompatibility frequently exists between a driver s desire to comply with the yellow-light-phase indication and his/her encountered constraints. Inspired by the pioneering GHM model, Olson and Rothery (6) conducted field observations at five intersections and found that drivers tend to take advantage of the long yellow-light phase and view it as an extension of the green phase. Their research concluded that driver behavior does not seem to be affected by the yellowlight phase duration, especially since most motorists do not even know the typical phase duration. The other dilemma, termed as Type-II Dilemma was proposed to accommodate the problem of indecision when both stopping and passing maneuvers can be executed. It defines the dilemma zone as the range in which 10 to 90 percent drivers decide to stop (7). Zeeger et al. (8) also proposed a measuring method termed as "option zone" in which 90% vehicles stop and 10% go under the condition of stochastic traffic distribution. Since the 1970s, dilemma zone protection systems have been deployed at the actuated intersections to mitigate the safety problems of dilemma zones. An excellent review of the related work was provided by Bonneson et al. (9). However, a major drawback of those dilemma zone protection systems is the assumed static dilemma zones. Transportation researchers in recent years began to realize that both the location and length of dilemma zones are dynamic in nature, and may vary with the complex interactions between the response of drivers, yellow phase duration, vehicle mechanical performances, intersection geometric features, and average traffic flow characteristics. For instance, Moon and Coleman (10) proposed a strategy to minimize the gate delay by adjusting rail-gate closing actions, based on the length and locations of dilemma zones on highway-rail intersections. McCoy and Pesti (11) designed a set of detection/warning strategies for safety improvements at high-speed intersections in response to the dynamic distribution of dilemma zones. For signalized intersections, several improvements of the dilemma zone protection

5 Liu, Chang, Tao, Hicks, and Tabacek 5 system have been proposed (9, 1). Instead of using an assumed desired speed, those approaches use the measured speed of a vehicle to determine its individual dilemma zone. However, those improvements did not fully address the probabilistic nature of the dilemma zone due to the measure error and driver preferences. A recent study by Tarko, et al. (13) proposed a framework to deal with the probabilistic dilemma zone problem by introducing the dilemma zone likelihood function as well as a method to optimize the green extension time. Xiang, et al. () performed an extensive numerical investigation of the dilemma zone dynamics under different driving populations and vehicle characteristics. Based on the survey results, they also classified driver behavior into several distinct patterns, and identified the potential key factors that may affect a driver s decision-making process during the yellow phase. However, due to the constraints of the sample size and the measurement method, their results are informative, but not sufficient for computing the dilemma zone distribution under different driving populations. Along the same line of research, this study will focus on the following critical subjects: Design of a reliable video-based measurement system to capture the critical data needed for driver classification and analysis of dilemma zones dynamics; Classification of drivers based on their responses to the yellow phase; Analysis of different dilemma zones for different driver groups at a target intersection; Recommendations of some strategies to address the safety issues associated with the distribution of dilemma zones. The paper is organized as follows: The data collection system for field observations is introduced in Section, including the key information to collect, observation and system validation procedures and results. Section 3 classifies the driving population into three distinct groups based on the response of drivers to the yellow phase, and extracts key characteristics associated with dilemma zone computation at each target intersection. Empirical results of the dynamic dilemma zone under different driver groups and yellow phase durations are presented in Section 4. Two safety improvement designs for eliminating the dilemma zones are briefly introduced in Section 5. Conclusions and future research needs are summarized in the last section.. DATA COLLECTION SYSTEM To capture the distribution of dilemma zones, this study has conducted field surveys at 6 typical signalized intersections in Maryland, and focused on collecting the following key information: Acceleration/deceleration rates of drivers before and after a yellow phase; Distance and expected time to the stop-line when drivers perceive the commencement of a yellow phase; The speed distribution of different driving populations in response to a yellow phase. In order to measure the above information reliably, this study has developed a videobased data collection system, as shown in Figure, which has the following functions: Precisely tracking each individual vehicle trapped in the yellow phase; Computing the exact distance and time for a vehicle to reach the stop-line from the start of a yellow phase;

6 Liu, Chang, Tao, Hicks, and Tabacek 6 Speed Yellow phase starts Speed Evolution Time 1 Time Time 3 Time 4 Time 5 Time Time 7 Time 8 Speed Trap Reference Points Stop Line Camera Location (a) (b) FIGURE A video-based data collection system

7 Liu, Chang, Tao, Hicks, and Tabacek 7 Measuring the speed evolution without influencing the behavior of drivers during a yellow phase; The key idea of the proposed system is to superimpose reference lines over the video image and measure a vehicle s travel times between these lines sequentially to obtain the speed evolution profile. The distance between two adjacent reference lines (i.e., speed trap length) has been optimized to minimize the potential measurement errors under given operational conditions (14). One can superimpose reference lines over the video image through a specially-designed computer program. The time when vehicles reach the reference line and the starting time of a yellow phase are also recorded by the program for extraction of the speed evolution profile before-and-after a yellow phase. Figure 3 illustrates the entire observation procedure with the proposed measuring system. FIGURE 3 Observation procedures of the video-based measuring system To evaluate the accuracy of the proposed system for speed measurements, this study has also conducted a field test at the intersection of MD 650 and Metzerott Road with a Nissan Infinity Q45 instrumented with a CAN message converter. The CAN message converter is a measuring device which can convert the actual speed to the precision of ± mph, and one can connect it to a laptop computer via a serial cable to display the speed of the experimental vehicle in a time frame of every 0.01 second. The speed data from the CAN message converter are deemed as the true speed, and used as the basis for evaluating the accuracy of the data collected from the proposed video-based system. The field validation consists of 4 trials over the test site with six different entry

8 Liu, Chang, Tao, Hicks, and Tabacek 8 speeds (0-5, 5-30, 30-35, 35-40, 40-45, mph), and 4 trials ( for pass, for stop) for each speed level. There are a total of 180 speed records ( pass plus stop records) for the system validation. As shown in Figure 4, there exists a high correlation between the measured speeds and the actual speeds (by CAN), which indicates a high accuracy of those speeds measured with the developed video-based method. Video(mph) Video(mph) Video(mph) y = x R = " Pass" t r i al s CAN( mph) y = x R = " St op" t r i al s CAN( mph) y = x R = (a) (b) Al l t r i al s CAN( mph) (c) FIGURE 4 Speed measurements by video versus the CAN converter

9 Liu, Chang, Tao, Hicks, and Tabacek 3. CLASSIFICATION OF DRIVING POPULATION This study has collected a total of 1,13 observations of individual driver responses over the yellow phase with the aforementioned video-based measuring system. As stated previously, driver behavior and characteristics at signalized intersections are not uniformly distributed, which will definitely affect the distribution of the dilemma zones. For convenience of analysis, this study has first classified the driving population at each sample intersection into three distinct groups: aggressive, conservative, and normal, based on their response to a yellow phase, and then measuring their key characteristics, such as the approaching speed and distance to stop-line when the yellow phase starts, average acceleration/deceleration rates after the yellow phase, and their approximate perception-reaction times. Classification of Driver Behavior In this study, all drivers observed at each intersection are classified into the following 3 groups: Group 1: Conservative stop Drivers who took the stop action even though they could have proceeded through the intersection during the yellow phase (i.e., the driver makes a stop even his/her distance-to-stop-line x d is less than the critical distance d c ); Group : Normal Drivers who took the stop action when x d > dc or the pass action when x d < d c ; Group 3: Aggressive pass Drivers who aggressively passed the intersection during the yellow phase even though they were quite far away ( x d > dc ). The critical value d c for driver classification can be estimated through a binary logit procedure (15) for each surveyed intersection based on the observations of each driver s distance-to-stop-line and response when the yellow starts. The classification results for all the six surveyed intersections as well as the critical distances are summarized in Table 1. It is noticeable that for all surveyed intersections, the driving population is not uniform and can be classified into different groups. The above classifications will be further used as the basis for estimating the dilemma zone for each driving group. TABLE 1 Driver classification results Surveyed Intersections (a) Critical distance-to-stop-line Yellow Cycle Length Duration(sec) (sec) Critical distance d c (ft) 193@ ft 650@Metzerott ft Randolph@Glennian ft 410@Belcrest ft 410@Adelphi ft 193@Mission ft

10 Liu, Chang, Tao, Hicks, and Tabacek 10 (b) Classification Results Surveyed Total Aggressive Conservative Normal Intersections Samples Pass Stop Randolph@Glennian @Belcrest @Adelphi @Mission Summary TABLE Speed difference analyses among driving groups Surveyed Average Speed/Std. Percentage Above Paired-t Group Intersections (mph) Average Traffic Ratio A-Pass* 41.05/ % @01 Normal 35.39/5.13 0% C-Stop* 3.35/ % A-Pass 38.74/ % @Metzrott Normal 34.13/6.9 0% C-Stop 30.00/ % A-Pass 5.5/ % 8.16 Randolph@Glennian Normal 45.91/4.59 0% C-Stop 40.81/ % A-Pass 38.09/ % @Belcrest Normal 31.19/ % C-Stop 9.55/ % A-Pass 38.70/ % @Adelphi Normal 30.49/ % C-Stop 7.1/ % A-Pass 54.40/ % @Mission Normal 44.15/ % C-Stop 41.00/ % * A-Pass means aggressive pass group, and C-Stop means conservative stop group.

11 Liu, Chang, Tao, Hicks, and Tabacek 11 Key Characteristics Associated with Driving Groups Based on the classification results, this study has compared the following key characteristics among driving groups: Approaching speed the speed of a vehicle when the yellow phase starts; Average acceleration/deceleration rates after the yellow phase; Perception-reaction time to the yellow phase. As shown in Table, at all the observed intersections, the aggressive-pass group usually executes an approaching speed about 10-0% higher than the average traffic flow speed, while the conservative-stop group averagely exhibits an approaching speed about 10-15% lower than the average traffic flow speed. The speed difference between different groups has been verified with the pair-t test. The mean values as well as the standard deviations of the acceleration/deceleration rates during the yellow phase for each driving group are summarized in Table 3. These empirically observed values, rather than the maximum theoretical values, can reflect the actual acceleration/deceleration maneuvers of vehicles among different driving groups after the yellow phase, and offer the basis for computing the actual dilemma zone distribution. A driver s perception-reaction time in response to YELLOW is also a critical factor that affects the dilemma zone distribution at signalized intersections. Unfortunately, the perception-reaction time of most drivers is quite short and difficult to observe. The proposed measuring system offers a convenient way to approximate a driver s response time with his/her speed profile (14), which is approximately equal to a theoretical perception-reaction time. The perception-reaction time analysis was made based on the entire sample size, and the mean values as well as the standard deviations are also summarized in Table DEMONSTRATION OF DYNAMIC DILEMMA ZONES Note that with the above analyses one can effectively obtain the approaching speed, acceleration/deceleration rates, and response time of drivers at a target intersection. These critical data are essential behavioral information for estimating the dilemma zone of each target driving group. In this paper, the dilemma zone distributions for different driving groups are estimated with Eq. (1) at each of those six intersections under the following three scenarios: Estimation using the set of parameters with theoretical values (see Table 4a) recommended by the ITE handbook (3) and with the actual yellow duration from the field observation; Estimation using the set of parameters measured from field studies (see Table 4b) with the proposed video-based system and the actual yellow duration; Estimation using the set of parameters measured from field studies (see Table 4b) with the proposed video-based system and an extended yellow duration. Those parameter values used for estimating the dilemma zones at all observed intersections are summarized in Table 4, and the results of the dilemma zone distributions are shown in Figure 5-7. Note that in Figure 5, all six observed intersections exist no dilemma zones (denoted as the dark bar in the figure) if the existing practice and the theoretical values for all key parameters (e.g., theoretical acceleration/deceleration rates and reaction times of normal drivers) are used in the computation.

12 Liu, Chang, Tao, Hicks, and Tabacek 1 TABLE 3 Field measured acceleration/deceleration rates and drivers response times (a) Field measured acceleration/deceleration rates Surveyed a/c rates A-Pass Normal C-Stop Intersections after yellow ( ft / sec ) ( ft / sec ) ( ft / sec ) 193@01 650@Metzrott Randolph@Glennian 410@Belcrest 410@Adelphi 193@Mission acceleration deceleration acceleration deceleration acceleration deceleration acceleration deceleration acceleration deceleration acceleration deceleration 0.39/ / /1.51* -4.93/1.9* -4.93/ / / / /.3* -5.10/1.0* -5.10/ / / / /3.5* -6.94/1.59* -6.94/ / / / /.04* -4.17/1.31* -4.17/ / / / /1.46* -4.30/1.4* -4.30/ / / / /.46* -5.87/1.48* -5.87/ /1.78 * Use the same values as the Normal group. (b) Field measured drivers response to YELLOW Driving Group Applicable Sample Size Aggressive Pass 64 Normal 538 Conservative Stop 78 Reaction time Mean 1.86s Std. 1.6s Mean 1.86s Std. 0.7s Mean.3s Std. 1.15s

13 Liu, Chang, Tao, Hicks, and Tabacek 13 TABLE 4 Parameter values applied in the computation of dilemma zones (a) Theoretical parameter values by the ITE manual Surveyed Intersections 193@01 650@Metzrott Randolph@Glennian 410@Belcrest 410@Adelphi 193@Mission Group ( a 1 ft /sec ) ( a ft /sec ) v 0 (mph) (sec) w (ft) L (ft) 1 (sec) (sec) A-Pass Normal C-Stop A-Pass Normal C-Stop A-Pass Normal C-Stop A-Pass Normal C-Stop A-Pass Normal C-Stop A-Pass Normal C-Stop (b) Field measured values Surveyed Intersections 193@01 650@Metzrott Randolph@Glennian 410@Belcrest 410@Adelphi 193@Mission Group ( a 1 ft /sec ) ( a ft /sec ) v 0 (mph) (sec) w (ft) L (ft) 1 (sec) (sec) A-Pass Normal C-Stop A-Pass Normal C-Stop A-Pass Normal C-Stop A-Pass Normal C-Stop A-Pass Normal C-Stop A-Pass Normal C-Stop

14 Liu, Chang, Tao, Hicks, and Tabacek 14 MD 01 MD Rd. MD Rd. MD Rd. Randolph Rd. MD Dr. FIGURE 5 Dilemma zone estimation using theoretical parameter values

15 Liu, Chang, Tao, Hicks, and Tabacek 15 MD 01 MD Rd. MD Rd. MD Rd. Randolph Rd. MD Dr. FIGURE 6 Dilemma zone estimation using field measured parameters

16 Liu, Chang, Tao, Hicks, and Tabacek 16 MD 01 MD Rd. MD Rd. MD Rd. Randolph Rd. MD Dr. FIGURE 7 Dilemma zone distribution under the impact of extended yellow phase

17 Liu, Chang, Tao, Hicks, and Tabacek 3 In contrast, as shown in Figure 6, dilemma zones exist at all observed intersections if field measured parameter values are applied in the computation. For instance, at the intersection of MD193@MD01, the dilemma zone for the conservative driver group is distributed from ft to 9.8ft to the stop-line with a range of 68.65ft, while the dilemma zone for the aggressive driver group has a wider and upstream range from 19.4ft to 43.6ft to the stop-line with a length of 04.ft. Even for the normal group, there exists the dilemma zone actually of ft (31.51ft ft). Similarly, at all other five intersections, the dilemma zone actually exists and varies with different driving populations. In general, aggressive drivers tend to encounter a wider dilemma zone with a location near the upstream of the approach than other driver groups, while conservative drivers are more easily trapped in the dilemma zone located at the downstream part of the approach. This study has also evaluated the impact of an extended yellow duration on reducing or eliminating the dilemma zones at signalized intersections. In this case, the yellow phases at all intersection are extended to 6 seconds to see their impact on the distribution of dilemma zones. As shown in Figure 7, although the dilemma zones for all driving groups are reduced or eliminated significantly, there are still some driving groups who will encounter a dilemma zone even with the yellow duration of 6 seconds. For example, at the intersection of MD193@MD01, after extending the yellow phase from the current 4.5 seconds to 6 seconds, the dilemma zone for the conservative driver group disappears. However the dilemma zones for the normal and aggressive driver groups still exist, although significantly reduced from ft and 04.ft to 61.51ft and ft, respectively. The same impact exists at the intersections of Randolph Rd.@Glenallan Rd. and MD193@Mission Dr. after extending their current yellow durations to 6 seconds. For the intersections of MD650@Metzerott Rd., MD410@Belcrest Rd., and MD410@Adelphi Rd., their dilemma zone distributions for all driver groups are not eliminated after the extension of the yellow phase. The above analysis of dilemma zones shown in Figure 5-7 can reflect the following findings: For all six observed intersections, the length and the location of their dilemma zones vary with the speed of the approaching vehicles, driver reaction times, and vehicle acceleration/deceleration rates of different driving populations; There exists significant differences between the theoretically estimated and the actual distributed dilemma zones; Extension of the yellow phase alone may not eliminate all the dilemma zones. 5. POTENTIAL APPLICATIONS OF THE RESEARCH RESULTS As evidenced in the above empirical results, simply extending the yellow phase will not eliminate all the dilemma zones due to their dynamic nature. To contend with the safety issues caused by the distribution of those dilemma zones, one can apply the research results in the following two types of safety improvement designs: The Type-I design consists of the driver behavior analysis module, vehicle detection module, and the signal control module. It is proposed to ensure that those drivers trapped into the dilemma zone can receive an extended yellow or all-red phase to clear the intersection safely (see Figure 8a). The vehicle detection module provides the system with the target vehicle s speed and position information. The driver behavior analysis module can then determine whether this vehicle could be trapped into a dilemma zone. The signal control module will be activated to extend the red-clearance time and may issue a ticket to the driver

18 Liu, Chang, Tao, Hicks, and Tabacek 18 for red light violation if he/she decides to run through the intersection. Driver Behavior Analysis Module Driver Classification Signal Control Module Vehicle Detection Module Signal Controller Reduce Speed Sign Dilemma zone range Extende d All-red (a) Type I design Driver Behavior Analysis Module Classification & Prediction Module Dilemma zone distribution module Reduce Speed Sign Vehicle Detection System Warnin Signal Controller Dilemma zone segmentation Extended All-red (b) Type II design FIGURE 8 Safety improvement designs to eliminate the dilemma zones

19 Liu, Chang, Tao, Hicks, and Tabacek 19 Compared with Type-I, the Type-II design adds the classification and prediction module as well as the dilemma zone distribution module for different driver groups (see Figure 8b). Once a target vehicle is approaching the intersection, the classification and prediction module will identify the location of the dilemma zone for the target driver. With such a function, the system can precisely classify drivers and identify the difference in their potential to encounter dilemma zones. 6. CONCLUSIONS The paper has presented the results of our empirical study on the distribution of dilemma zones for different groups of drivers at signalized intersections. Using a specially designed video-based system, this study has conducted extensive field observations of 1,13 drivers responses to a yellow phase at six intersections of high accident frequency, including all critical data such as the speed evolution during the yellow phase, the acceleration/deceleration rates, and the approximate reaction time to an encountered yellow phase. The empirical results have clearly indicated the existence of multiple dilemma zones at all six intersections, and the location and range of those dilemma zones vary with the behavior of the driving population. Aggressive driver group is more likely to encounter a wide range of dilemma zone. Our numerical analyses have further evidenced the substantial differences between the theoretical dilemma zone based on the existing practice and the actual distribution of such zones. In brief, this study has concluded that: The video-based measuring system developed in the study is cost-effective for measuring speed evolution at a signalized intersection, which is necessary in computing the speed, acceleration/deceleration rates, and the response time of different driving populations; The length and the location of the dilemma zone vary with the speed of the approaching vehicles, driver reaction times, vehicle acceleration/deceleration rates, and the yellow phase duration; Significant discrepancies exist between the theoretically computed distribution and the actual distribution of dilemma zones at signalized intersections; Extension of the yellow phase alone may not eliminate all dilemma zones at intersections having a high speed approaching flows.

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